A heat engine is involved with exchange of heat
Question:

A heat engine is involved with exchange of heat of $1915 \mathrm{~J}$, $-40 \mathrm{~J},+125 \mathrm{~J}$ and $-Q \mathrm{~J}$, during one cycle achieving an efficiency of $50.0 \%$. The value of $Q$ is :

1. $640 \mathrm{~J}$

2. $40 \mathrm{~J}$

3. $980 \mathrm{~J}$

4. $400 \mathrm{~J}$

Correct Option: , 3

Solution:

(3) Efficiency, $\eta=\frac{\text { Work done }}{\text { Heat absorbed }}=\frac{W}{\Sigma Q}$

$=\frac{Q_{1}+Q_{2}+Q_{3}+Q_{4}}{Q_{1}+Q_{3}}=0.5$

Here, $Q_{1}=1915 \mathrm{~J}, Q_{2}=-40 \mathrm{~J}$ and $Q_{3}=125 \mathrm{~J}$

$\therefore \frac{1915-40+125+Q_{4}}{1915+125}=0.5$

$\Rightarrow 1915-40+125+Q_{4}=1020$

$\Rightarrow Q_{4}=1020-2000$

$\Rightarrow Q_{4}=-Q=-980 \mathrm{~J} \Rightarrow Q=980 \mathrm{~J}$